[time-nuts] Designing an embedded precision GPS time

Bob kb8tq kb8tq at n1k.org
Wed Nov 1 18:09:24 EDT 2017


> On Nov 1, 2017, at 1:11 PM, tnuts at joshreply.com wrote:
>> While crystal curves are indeed cubic, there are higher order terms in 
>> the curve. The “why” is something people get to write papers on. If you 
>> are trying to compensate to tight specs, you will see all sorts of 
>> stuff. It is not at all uncommon to see >9th order curves residual curves. Indeed some of that is from residuals in the compensation circuit as well as from the crystal.
> I’ve been trying to research this very topic!
> Can you point to some of these papers?

The Frequency Control Symposium has papers going back > 50 years on crystals and how to 
cut them from raw quartz bars. Plan on spending a few million dollars to get set up to do this well. 
Something in the $5M is likely the “going rate” these days for a basic line, even with some of it
bought surplus. 

> I am trying to build the most accurate fee running, low power time base I can. I am using an MCU, 32768Khz watch crystals,

Which are very low precision crystals by their very nature…..

> 0.5C accuracy temp sensor, lots of thermal bringing between them, and mass around them.

Which is pretty loose by todays standards. You can get parts that will do better than that. 

> The idea is to measure the frequency shift at all temps in the range, and even in both directions (hopefully to capture some hysteresis)

Keep in mind that your hysteresis runs need to be at multiple speeds and over multiple temperature ranges. The results vary with 
both promoters.  

> for each unit and then use that database to compensate in software once the system is free running. 

Assuming you have a “normal” watch crystal, you can get into slopes well over 10 ppm / C without going to crazy extremes. That
and your 0.5 C resolution is going to have a pretty big impact. 

> I am trying to beat existing products like the Dallas DS3231 and Micro Crystal RV-8803-C7-32.768kHz-3PPM-TA-QC, which use (I think) a similar strategy. I’m hoping I can beat them by using more accurate temp tensing, longer and more exhaustive calibration effort, and anything else possible! 

I’d say it’s unlikely. 

> Can you give a quick explanation (or point to reference material) covering the fundamental limits to XTAL compensation accuracy, and how to get there?

The FCS proceedings have a number of papers. The basics depend a lot on the type of crystal you have and the net result you are after. If you must 
have the output on frequency that leads in a different direction than if you just want an accurate one second tick. For example, with the one second tick, 
you can drop (or add) cycles in your divider. If the oscillator is at 10 MHz, the net result will always be within 100 ns. For something like NTP, there
is no real advantage going past that point. You can accumulate error over a long period. That allows very good stability over the long term. 

If you need low power and proper frequency, a thermistor resistor network driving a varicap diode is the classic answer. You generate a cubic voltage
function over temperature. It is the “required signal” to tune the oscillator on frequency. The components in the network are evaluated and adjusted with multiple 
temperature runs. The software to make it all work is generally the “top secret” IP of the people making the TCXO.

A brute force approach using a good temperature sensor (say an RTD) and a good ADC is possible. You can get into the low mili C range with this sort of
setup. Pairing that with a good low frequency overtone crystal can do pretty well. There are also multi mode ostillators that head in the same direction. There
are many twists and turns. A starting engineer generally takes something in the 5 year range to come up to speed on most of them. 

> That is, if I had an infinitely precise temp sensor and an infinite amount of time to characterize an XTAL, what would be limits to how accurately I could temp compensate it?

Well, aging is one obvious issue. ADEV is another. A reasonable goal for aging would be in the low parts in 10^-11 per day range. Good ADEV at 1,000 seconds 
would be at least that good. The electronics to make it all happen might use as much power as a low power OCXO …. Managing temperature in a TCXO like 
device below 1x10^-10 is unlikely.  Figure the crystal used would be > $100 in volume. Single piece (if you could buy one) might be over a thousand dollars. 

> Also, what are the limits of characterizing and compensating for aging?

Low parts in 10^-11 per day on a “production” basis if cost is not a consideration. It also depends quite a bit on the constraints you put on the problem. (how many
days on power, what sort of environment, ….)

> What other sources of inaccuracy would I need to consider?

There are *many*. How many years do you have to study the various topics? Thermal gradients are one that will bother you. 

Again, the FCS papers are a good start. Best to find a library  with free access. They are a bit expensive on DVD. 


> Thanks!!!
> -josh
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